Mathematics College

A given line has the equation 10x + 2y = −2.

What is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)?

Answers

Answer 1
10x + 2y = -2

2y = -10x -2

y = -5x - 1 (slope is -5 and a parallel line will have the same slope)


y = mx + b

slope(m) = -5

12 = -5(0) + b

12 = 0 + b

12 = b

so the parallel line is y = -5x + 12

hope this helps, God bless!

Related Questions

What is the number 0.093 expressed in Scientific notation?
A. 9.3 * 10^2
B. 0.93 * 10^1
C. 9.3 * 10^-3
D. 9.3 * 10^-2

Answers

0.093 expressed in Scientific 
=
9.3 x 10^-2

answer
D. 9.3 * 10^-2

Option D is correct. 0.093 can be expressed in scientific notation as [tex]9.3 \times 10^{-2}[/tex].

To express the number 0.093 in scientific notation, we need to determine the coefficient and exponent.

0.093 can be written as 9.3 multiplied by a power of 10.

Since 0.093 is less than 1, the exponent should be negative.

To shift the decimal point to the right to form the original number, we move it three places to the right:

[tex]0.093 \rightarrow 9.3 \times 10^{-2}[/tex]

Therefore, 0.093 can be expressed in scientific notation as [tex]9.3 \times 10^{-2}[/tex], option D is correct.

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A new iPhone user receives an average of 4.2 phone calls per hour. The calls occur randomly in time so if X = the number of calls received in an hour, then we can assume that X has a Poisson distribution with parameter λ = 4.2. Let Y = the number of phone calls received in a day. Assume all necessary independence in the following.
a. Y also has a Poisson distribution. What is the λ for Y?

b. What is the standard deviation of X?

c. What is the standard deviation of Y?

d. What is the probability that no calls are received in an hour?

e. What is the probability that more than 120 calls are received in a day?

f. What is the probability that Y is between 90 and 110 inclusive? (i.e. 90 ≤ Y≤110)

g. What is the variance of square root of 2Y?

h. Assume this distribution holds for all hours and days and that one call is independent from another. What is the probability that 120 or fewer calls are received for every day of this week? (Assume appropriate independence

Add any comments below.

Answers

Part A:

Given that Y is the number of phone calls received in a day and that a new iPhone user receives an average of 4.2 phone calls per hour.

Thus, the average number of phone calls received in a day is 4.2 * 24 = 100.8

Therefore, the λ for Y is 100.8



Part B:

The standard deviation of a Poisson distribution is given by

[tex]\sigma=\sqrt{\lambda}[/tex]

Thus, the standard deviation of X is given by

[tex]\sigma=\sqrt{4.2}=2.05[/tex]

Therefore, the standard deviation of X is 2.05.



Part C:

The standard deviation of Y is given by

[tex]\sigma=\sqrt{100.8}=10.04[/tex]

Therefore, the standard deviation of X is 10.04.



Part D:

The probability of a Poisson distribution is given by

[tex]P(X=x)=e^{-\lambda} \frac{\lambda^x}{x!} [/tex]

where, x is the number of occurence of the event in the given period.

Thus, the probability that no calls are received in an hour is given by

[tex]P(X=0)=e^{-4.2} \frac{(4.2)^0}{0!} =0.015[/tex]

Therefore, the probability that no calls are received in an hour is 0.015



Part E:

We approximate the Poisson distribution using Normal distribution by noting that for a Poisson distribution

[tex]\mu=\lambda \\ \\ \sigma^2=\lambda \\ \\ \sigma=\sqrt{\lambda}[/tex]

The probability of a normal distribution is given by

[tex]P(X\ \textless \ x)=P\left(z\ \textless \ \frac{x-\mu}{\sigma} \right)[/tex]

Thus, the probability that more than 120 calls are received in a day is given by

[tex]P(X\ \textgreater \ 120)=1-P(X\leq120) \\ \\ =1-P\left(z\leq \frac{120-100.8}{10.04} \right)=1-P(z\leq1.912) \\ \\ =1-0.97208=0.0279[/tex]

Therefore, the probability that more than 120 calls are received in a day is 0.0279



Part F:

We also approximate this using Normal distribution

The probability of a normal distribution between two value (a, b) is given by

[tex]P(a\ \textless \ X\ \textless \ b)=P\left(z\ \textless \ \frac{b-\mu}{\sigma} \right)-P\left(z\ \textless \ \frac{a-\mu}{\sigma} \right)[/tex]

Thus, the probability that Y is between 90 and 110 inclusive is given by

[tex]P(90\leq X\leq 110)=P\left(z\leq \ \frac{110-100.8}{10.04} \right)-P\left(z\leq \frac{90-100.8}{10.04} \right) \\ \\ =P(z\leq0.916)-P(-1.076)=0.82025-0.14103=0.67922[/tex]

Therefore, the probability that Y is between 90 and 110 is 0.67922



Part G:

The variance of aY is given by

[tex]Var(aY)=a^2Var(Y)[/tex]

Thus, the variance of [tex] \sqrt{2} Y[/tex] is given by

[tex]Var( \sqrt{2} Y)=( \sqrt{2} )^2Var(Y)=2(100.8)=201.6[/tex]

Therefore, the variance of [tex] \sqrt{2} Y[/tex] is 201.6



Part H:

We approximate this using Normal distribution

The probability of a normal distribution is given by

[tex]P(X\ \textless \ x)=P\left(z\ \textless \ \frac{x-\mu}{\sigma} \right)[/tex]

Thus, the probability that 120 or fewer calls are received in a day is given by

[tex]P(X\leq120)=P\left(z\leq \frac{120-100.8}{10.04} \right) \\ \\ =P(z\leq1.912)=0.97208[/tex]

Since, this distribution holds for all hours and days and one call is independent from another. Assuming that there are seven days in a week.

The probability that 120 or fewer calls are received for every day of this week is given by

[tex](0.97208)^7=0.8202[/tex]

Therefore, the probability that 120 or fewer calls are received for every day of this week is 0.8202

The ordered pair (2, 1) is a solution of a direct variation equation. Write the equation and identify the constant of variation.

Answers

A direct variation equation takes the form "b = ka," where the k is the constant of variation. In this case, 1 (b) is one-half as large as 2 (a), so the constant will be 0.5. This would allow the equation to be written as "b = 0.5a," and the constant of variation in this equation is 0.5.

Integers contain the whole numbers.true or false

Answers

True, Integers mean "whole", and it cannot be a fraction or decimal


hope this helps
true , hope this helps :)

Simplify 3 + c (8n + 4) + 9n

A. 49n + 20
B. 3+33n
C. 25n + 11
D. 19n + 7

Answers

c is the answer to your question

Well first you need to distribute the (c) to the 8n+4. So then you you would get 8nc+4c+9n+3. Not unless that (c) is suppose to be a number.

Suppose △DEF≅△MNO.
Which congruency statement is true?

A) DF≅NO
B) DE≅MN
C) EF≅MN
D) EF≅MO

Answers

the answer is b. would u like to see steps or are you good?
Final answer:

When triangles are congruent, their corresponding sides and angles are the same. Hence in congruent triangles △DEF and △MNO, side DF is congruent to side MN, thus option B) DE≅MN is the correct answer.

Explanation:

In the case of congruent triangles, the corresponding sides and angles are essentially the same. Therefore, we must match up the corresponding sides. A correct statement would be that side DF, from the first triangle, is congruent to side MN, from the second triangle. Hence the correct option is B) DE≅MN.

Additionally, DE would be congruent to MN, and EF would be congruent to NO, completing the congruence between triangles △DEF and △MNO.

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I don't get why price(max)=$80
Can someone help me

Answers

check the picture below.

as a matter of elasticity, if you sell 100 popsicles for $1, you get a revenue of $100.

However, if your price goes to $5 per popsicle, then folks will begin to find it too expensive and won't be buying 100, but just 15, so, even though $5 is a higher price, 5 * 15 is a much smaller revenue than 1 * 100.

Stuck on this question. Any help would be appreciated.

Answers

Solving the 2nd equation for r results in
         10-2h
r = --------------
             5
                    (10-2h)^2
Then r^2 = ----------------
                         25

Substitute this r and this r^2 into the first equation and simplify.  This will result in a formula for V as a function of h (V in terms of h).

Complete the sentence using one of the words below in 10/6 the 10 is the

Answers

The 10 Is The Numerator

tep 1: –10 + 8x < 6x – 4 Step 2: –10 < –2x – 4 Step 3: –6 < –2x Step 4: ________

Answers

Step 4: 3>x. (The sign flips because you divided a negative)
I hope this helps love! :)

How many times dose 63 go into 272? THANK YOU SO MUCH FOR ANSWERING,IF YOU DID!!!!!!!

Answers

Let's write this problem as an expression: 272 ÷ 63
Now, it is just division, and we can divide the two numbers to get 4.317...
However, the question only asks for how many times 63 goes into 272, so the answer would be that 63 goes into 272 four times. Hope this helps and have an awesome day!

Can someone please solve this?

Answers

multiplicity of a root means, is there that many times.

[tex]\bf \begin{cases} x=3\implies &x-3=0\\ x=2\implies &\begin{cases} x-2=0\\ x-2=0\\ x-2=0 \end{cases} \end{cases} \\\\\\ (x-3)(x-2)~~(x-2)(x-2)=\textit{original polynomial} \\\\\\ (x^2-5x+6)~~(x^2-4x+4)=y \\\\\\ x^4-4x^3+4x^2-5x^3+20x^2-20x+6x^2-24x+24=y \\\\\\ 1x^4-9x^3+30x^2-44x+24=y[/tex]

Which expression makes the equation true? X^8 = ( )^2

Answers

x^8 = ()^2

x^8 = (x^4)^2

x^8 = x^8

inside the parethesis is x^4

hope this helps
(a^m)^n = a^(mn)

x^8 = (x^4)^2 = x^(4 * 2) = x^8

Answer: (x^4)^2

Jennifer's grandmother buys carrots at the farm stand. She and her 3 grandchildren equally share the carrots. The total weight of the carrots she bought is 28 kilograms. How many kilograms of carrots will Jennifer get ?

Answers

since they share it equally
28/4=7

Write the equation for the following relation. Include all of your work in your final answer. Submit your solution. P = {(x, y): (1, 0), (2, 4), (3, 8), (4, 12), . . .}

Answers

First, we will notice that while the value of x increases by 1, the corresponding value of y increases by 4. This means that this is a linear relation.

The general equation for linear equations is : y = mx + c where m is the slope and c is the y-intercept

To get the slope, we will need to use two points. Let's take the first and the last points: (1,0) and (4,12)
The slope is calculated as: (y2-y1) / (x2-x1)
Use the chosen points to substitute in the equation and get the slope as follows:
m = (12-0) / (4-1) = 12/3 = 4

Now, the equation of the line became: y = 4x + c

The given points all satisfy the equation of the line, we can use any of them to substitute in the equation and get the value of c.
For instance, I will use the first point: (1,0)
y = 4x + c
0 = 4(1) + c
c = -4

The equation of the line is:
y = 4x - 4

The table shows the steps for solving the given inequality for x.

−3(4−6x)
Select the reason for each step from the drop-down menus.

Answers

step                                      justification

- 3 (4 - 6x) < x + 5            

- 12 + 18x < x + 5                 distributive property (to solve the left side)

-12 + 17x < 5                        subtraction property of equality (to transpose x
                                             from right to left side)

                                              subtraction of like terms (18x - x = 17x)

17x < 17                                addition property of equality (to tranpose - 12
                                              from left to right side)

                                              addition of like terms (12 + 5 =17)

x < 1                                      division property of equality



Answer:step                                      justification

- 3 (4 - 6x) < x + 5            

- 12 + 18x < x + 5                 distributive property (to solve the left side)

-12 + 17x < 5                        subtraction property of equality (to transpose x

                                            from right to left side)

                                             subtraction of like terms (18x - x = 17x)

17x < 17                                addition property of equality (to tranpose - 12

                                             from left to right side)

                                             addition of like terms (12 + 5 =17)

x < 1                                      division property of equality

Step-by-step explanation:

At a dog park there are 12 golden retriever and 20 poodles what is the ratio of golden retriever to poodles

Answers

You need to find a number that 12 and 20 share so you go through all the number starting with 1 and go until you can find one so I'll use the numbers 2 and 4. Gives you two options.
12/2=6
20/2=10
6:10

12/4=3
20/4=5
3:5

State the slope and the y-intercept of each given graph plz help i really dont know how to do this

Answers

For graph 1, the y-intercept is (0,1) and the slope is 1. 
For graph 2, the y-intercept is (0,4) and the slope is -1. 
For graph 3, the y-intercept is (0,-4) and the slope is -2.
For graph 4, the y-intercept is (0,-3) and the slope is 3/2.
For graph 5, the y-intercept is (0,4) and the slope is 2.
For graph 6, the y-intercept is (0,3) and the slope is -3/2.

(By the way, since the graphs aren't labeled as numbers, I went from left to right, and then down, and then left to right again).

Now, here's the explanation: 

Solving for y-intercept is easier than it sounds. All you need to do is mark the point where the line crosses the y-axis (vertical axis).

Solving for slope is just rise/run. For example, in graph one, the points on the line went up one and then to the right one.

So, 1/1 = 1. 

When a slope moves down or to the left, it will be negative. However, that's only if the rise OR run is down/left. If both are negative, the two will cancel each other out to make a positive. 

Hope this helped!! 

the sum of 2 3/5 + (-1/5) write in simplest form

Answers

The answer is 2 2/5. Need an explanation
2 2/5 that’s the answer

Shelly sells 5 bone shaped treats for $3.50 how much should she charge to a pack of 12 treats which proportion is needed to solve the problem

Answers

Hola en ese caso se realiza una regla de tres.
si shelly cobra 5 golosinas por 3.50 dolares, 12 golosinas a cuanto equivaldran.

(12x3.50)/ 5 = 8.4 dolares deberia cobrar

Answer

5/3.5and 12/x or d

what's the closest number to 27.8 * 9.8

Answers

280...round each number to the nearest whole number (27.8=28 and 9.8=10) then multiply and you will get 280
27.8 * 9.8  =  272.44

Closest whole number = 272.

Sampling is ordinarily used when the number of items comprising the population is relatively small.

Answers

I believe this statement is false, and that sampling is used when the number of items in a population are fairly large. One would use a sample to represent some form of measurement or test so that it can be applied to the larger number of same objects.

Plot the x- and y-intercepts to graph the equation. y=−12x−3

Answers

x-intercept: (1/4) ,0
y-intercept: (0, -3)

Keywords

x-intercept, y-intercept, linear equation, graphing tool

we know that

The y-intercept is the value of y when the value of x is equal to zero

The x-intercept is the value of x when the value of y is equal to zero

In this problem we have

[tex]y=-12x-3[/tex]    

Step 1

Find the x-intercept

For [tex]y=0[/tex]

find the value of x

[tex]0=-12x-3[/tex]

[tex]12x=-3[/tex]

[tex]x=-0.25[/tex]

The x-intercept is the point [tex](-0.25,0)[/tex]

Step 2

Find the y-intercept

For [tex]x=0[/tex]

find the value of y

[tex]y=-12*0-3[/tex]

[tex]y=-3[/tex]

The y-intercept is the point [tex](0,-3)[/tex]

Step 3

With the point [tex](-0.25,0)[/tex] and the point  [tex](0,-3)[/tex]

Plot the  linear equation

Using a graphing tool

see the attached figure      

therefore

the answer in the attached figure

how many square inches does an "11x13" area encompass

Answers

143 square inches          

Answer:

143 square inches

Step-by-step explanation:

The area of encompass is given by 11 * 13 inches.

Here the length = 11 inches and the width = 13 inches.

The length and width have different numbers, so the given figure is a rectangle.

Area of a rectangle = length * width

Area of the figure = 11*13

= 143 square inches

The unit for the area is "square"

The units are given in inches, therefore, it is 143 square inches.

Here again is the information about the prescription drug: there is a 10% chance of experiencing a sore throat (s) and a 30% chance of experiencing a fever (f). the information also states that there is a 6% chance of experiencing both side effects. what is the probability of experiencing neither of the side effects?

Answers

youve got a 94% chance of not experiencing it but a 90% chance of not experiencing a sore throat and a 70% cahnce of not experiencing a fever

Use addition to simplify the expression 6/x+6/3x . show all the steps necessary to write the expression with a common denominator and to simplify the expression

Answers

Common Denominator   is 3x 

we write 6/x as 18/3x So we have

18/3x + 6 /3x = 24/3x

simplifyiby dividing numerator and denominator by 3:-

Answer is 8/x

Two pounds of bananas cost $1.16 what would be the cost of 5pounds s of bananas

Answers

If 2 lb of bananas cost $1.16, then each pound costs $0.58.

0.58 * 5 = 2.9

So 5 lb of bananas will cost $2.90.

Hope this helps!
The cost of 5 lbs of bananas would be $2.90.

Y=2x^2-x-10 write in intercept form

Answers

y-intercept:  Let x = 0 and solve for y.  Then y =2(0)^2 -(0) - 10 = -10.  The y-intercept is (0,-1).

x-intercept:  Let y = 0 and solve for x.
Then 0 = 2x^2 - x - 10.  a=2, b= -1 and c = -10.
                 -(-1) plus or minus  sqrt[ (-1)^2 - 4(2)(-10)
Then x = ------------------------------------------------------------
                               2(2)
                  1 plus or minus sqrt(81)        1 plus or minus 9
          x = ----------------------------------- = ---------------------------
                                      4                                     4

Calculate the 2 x-values.  Let's call them "a" and "b."  Then the x-intercepts (there are 2) are

(a, 0) and (b, 0)

In a football game, the home team gained 8 yards in a running play. After that, the quarterback was sacked for a loss of 8 yards. On the next play, the quarterback threw a 25-yard pass for a touchdown. What was the final yardage gain on the play? Justify your answer.

Answers

25 yards because he gained 8 then lost 8

A map of a public park shows a circular pond. There is a bridge along a diameter of the pond that is 0.25 mi long. You walk across the bridge, while your friend walks halfway around the pond to meet you at the other side of the bridge. How much farther does your friend walk?

Answers

The circumference of a circle is pi times diameter, so half-way around the pond is (1/2)pi times diameter.

[tex]\frac{\pi}{2} = 1.57[/tex]

The difference between walking around the pond and walking across the bridge is: 1.57d - d = 0.57d

Plug in diameter of 0.25

0.25*0.57 = 0.14 miles
Final answer:

Your friend walks approximately 0.3925 miles farther than you along the curved path of the pond.

Explanation:

To find out how much farther your friend walks, we need to compare the distance along the bridge to the distance halfway around the pond. The bridge is a straight line across the pond, which is the same as the diameter of the pond. The diameter is 0.25 miles long. Your friend walks halfway around the pond, which is equivalent to walking half the circumference of the pond. The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. Since the bridge is the diameter, it is equal to 2 times the radius, or 2r. So the distance your friend walks is half the circumference or (1/2)(2πr) = πr. Since the diameter is 0.25 miles, the radius is half of that, or 0.125 miles. Plugging this into the formula, we find that your friend walks π(0.125) miles. To find a numerical approximation, we can use the fact that π is approximately 3.14, so your friend walks 3.14(0.125) miles. This simplifies to approximately 0.3925 miles. Therefore, your friend walks approximately 0.3925 miles farther than you along the curved path of the pond.

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